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Tesseract Love

I love these things…there’s something about them that I relate to the “self-transforming” aspects of another strange space. Watch as a four-dimensional object cuts through our limited three-dimensional perception:

Admit it. You can’t take your eyes off this object. This is a tesseract and as such is a 4 dimensional shape. Wait, though. We only live in three dimensions, don’t we? So although this object is beautiful, hypnotising almost – what on earth is it and what is it doing here, confounding our lovely three dimensions with its impertinent fourth? Strictly speaking, what you can see above is a two dimensional projection of a three dimensional simulation of a four dimensional tesseract, that’s what

…Think of the space with which you are familiar. Put simply; think of the ways in which you can move. There is left to right, forwards and backwards. Finally there is up and down. Three ways, three dimensions. You can pinpoint your location by working out your coordinates in those three directions.

…When you go to the fourth dimension (cue Twilight Zone music) you have another direction. That direction is (wait for it) at right angles to each and every one of the three original directions. If your head just exploded, don’t worry. That is quite a normal reaction. Just take it from me that the math works.

Tesseract 101 at Kuriositas.

Previously on TDG:

Editor
    1. long ago
      Some time ago I dealt with mapping n-dimensional connectivity to 2D networks, taking into consideration how close the corners should/should not be, and how short the edges should be.

      I tried to adjust the measurement of how good a solution is by selecting constant weight factors to the importance of corners and edges.

      It turns out that it can’t be done with constants, unfortunately I forget the mathematical proof. It’s not that it is hard, it is impossible.

      Some years later I was wondering if the problem becomes solvable (maybe even tractable) by using weight functions instead of weight constants. Haven’t persued the question, it is not obvious at all whether this would help. It is similar in spirit to what this guy Shu is doing with the universal constants. Strange.

  1. Cube 2?
    check out the awesomely lame movie Cube 2: Hypercube. Featuring a dude getting chewed up inside one of these things. Awesome! Cube 1 is worth checking out too.

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